The Lie Conformal Algebra of a Block Type Lie Algebra

Abstract

Let L be a Lie algebra of Block type over C with basis {L α,i | α, i ∈ Z} and brackets [L α,i , L β,j ] = (β(i + 1) − α(j + 1))L α+β,i+j . In this paper, we shall construct a formal distribution Lie algebra of L. Then we decide its conformal algebra B with C[∂]-basis {L α (w) | α ∈ Z} and λ-brackets [L α (w) λ L β (w)] = (α∂ + (α + β)λ)L α+β (w). Finally, we give a classification of free intermediate series B-modules.

On a class of infinite simple Lie conformal algebras

“…for any α, β ∈ Z. Note that this Lie conformal algebra is not simple and the free intermediate series modules of CL are studied in [14].…”

Loop Schrödinger–Virasoro Lie conformal algebra

“…In addition, Lie conformal algebras have close connections to Hamiltonian formalism in the theory of nonlinear evolution. The structure theory and representation theory of Lie conformal algebras were intensively studied (see, e.g., [1,3,4,6,7,[13][14][15][16][17]). In this paper, we investigate derivation algebras, second cohomology groups and some free modules over conformal algebras associated with loop algebras of the Schrödinger-Virasoro Lie algebra and its extended algebra.…”

Loop Heisenberg-Virasoro Lie conformal algebra

“…Two new nonsimple conformal algebras associated with the Schrödinger-Virasoro Lie algebra and the extended Schrödinger-Virasoro Lie algebra were constructed in [13]. The Lie conformal algebra of a Block type was introduced and free intermediate series modules were classified in [7]. The loop Virasoro Lie conformal algebra was studied in [15].…”